# Dumb speed of light question

how is it known that the speed of light (or any physical constant) is constant?

couldn't it be that it's changing at a slow rate? over a 15 billion year history, this adds up to a significant change in the speed of light.

if c* was the speed of light when t=0 and if it gets multiplied by a factor of 1.0000000001 every millenium, since there have been 15 million millenia (though that would be drawn into question if c is not constant), that would add up to 1.0000000001^(15 10^9)=4.5 times as fast now than it was when t=0.

## Answers and Replies

russ_watters
Mentor
When people talk about the speed of light being constant, they are talking about inertial frames of reference TODAY. 2 billion years ago? Not so sure - but there are reasons to believe that it hasn't changed much (if at all) during the aging of the universe. The reasons come from observing distant objects - thouth I can't remember offhand what they look at exactly to measure the speed of light.

Integral
Staff Emeritus
Science Advisor
Gold Member
The speed of light can be derived from Maxwells equations. This was done by Maxwell in the mid 1860s. From this set of equations which define our knowledge of Electromagnetism we have

$$c= \frac {1} {\sqrt {\mu_0 \epsilon_0}}$$

If you do very much looking at the many speed of light threads in these fourms you will find discussions of this.

right, so then the question is that how is it known that those constants referenced in your equation are constant?

secondly, does it matter?

Originally posted by phoenixthoth
right, so then the question is that how is it known that those constants referenced in your equation are constant?

secondly, does it matter?

We don't know that the electromagnetic factors are constants in time. We only suppose they are so. What matters is the cogency of the theory of relativity. This theory is not a theory that produces constancy of lightspeed; this theory produces relationships in space, time, mass, momentum and energy from the assumption of constant (and invariant) lightspeed. To get these relationships in a straight-forward manner, it is necessary that light exchanged between different moving observers behave this way. The results of relativity are expressed in so many of the phenomena of modern physics.

So, to put it briefly: we want to sustain the results of relativity and that is done most easily assuming that lightspeed is both constant and invariant (at least for short-enough periods of time). Over very long epochs of time it is another question.